hp-version time domain boundary elements for the wave equation on quasi-uniform meshes

Abstract

Solutions to the wave equation in the exterior of a polyhedral domain or a screen in ${\mathbb{R}}^3$ exhibit singular behavior from the edges and corners. We present quasi-optimal $hp$-explicit estimates for the approximation of the Dirichlet and Neumann traces of these solutions for uniform time steps and (globally) quasi-uniform meshes on the boundary. The results are applied to an $hp$-version of the time domain boundary element method. Numerical examples confirm the theoretical results for the Dirichlet problem both for screens and polyhedral domains.

arXiv comment41 pages, 11 figures

References in corpus (4)

• A priori error estimates for a time-dependent boundary element method for the acoustic wave equation in a half-space
• Boundary elements with mesh refinements for the wave equation
• Time domain boundary elements for dynamic contact problems
• On a preconditioner for time domain boundary element methods

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• Adaptive time-domain boundary element methods for the wave equation with Neumann boundary conditions